3 Mary takes over a small café. She will sell two types of hot drink: tea and coffee.
A coffee filter costs her \(\pounds 0.10\), and makes one cup of coffee. A tea bag costs her \(\pounds 0.05\) and makes one cup of tea. She has a total weekly budget of \(\pounds 50\) to spend on coffee filters and tea bags. She anticipates selling at least 500 cups of hot drink per week. She estimates that between \(50 \%\) and \(75 \%\) of her sales of cups of hot drink will be for cups of coffee. Mary needs help to decide how many coffee filters and how many tea bags to buy per week.

1. Explain why the number of tea bags which she buys should be no more than the number of coffee filters, and why it should be no less than one third of the number of coffee filters.
2. Allocate appropriate variables, and draw a graph showing the feasible region for Mary's problem. Mary's partner suggests that she buys 375 coffee filters and 250 tea bags.
3. How does this suggestion relate to the estimated demand for coffee and tea?